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Rationalizable Implementation of Social Choice Correspondences

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Abstract

A social choice correspondence (SCC) F is a mapping which associates with every state θ ∈ Θ a non empty subset of a set of outcomes. F is implementable in rationalizable strategies provided that there exists a mechanism such that for each state θ, the support of its set of rationalizable outcomes is equal to the socially desirable set F(θ). We find that r-monotonicity is a necessary condition for the rationalizable implementation of F. When there are at least three agents and F satisfies certain auxiliary conditions, r-monotonicity is also sufficient for rationalizable implementation. Finally, we show that a SCC which is never single valued is rationalizably implementable if and only if it satisfies r-monotonicity.

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  • Ritesh Jain, 2019. "Rationalizable Implementation of Social Choice Correspondences," IEAS Working Paper : academic research 19-A002, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    • Handle: RePEc:sin:wpaper:19-a002
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    Cited by:

    1. Guo, Huiyi & Yannelis, Nicholas C., 2022. "Robust coalitional implementation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 553-575.
    2. Takashi Kunimoto & Rene Saran & Roberto Serrano, 2020. "Interim Rationalizable Implementation of Functions," Working Papers 2020-23, Brown University, Department of Economics.
    3. Siyang Xiong, 2022. "Rationalizable Implementation of Social Choice Functions: Complete Characterization," Papers 2202.04885, arXiv.org.
    4. Ritesh Jain & Ville Korpela & Michele Lombardi, 2022. "Two-Player Rationalizable Implementation," CSEF Working Papers 660, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    5. Jain, Ritesh & Lombardi, Michele, 2022. "Continuous virtual implementation: Complete information," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    6. Xiong, Siyang, 2023. "Rationalizable implementation of social choice functions: complete characterization," Theoretical Economics, Econometric Society, vol. 18(1), January.
    7. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2021. "Rationalizable implementation in finite mechanisms," Games and Economic Behavior, Elsevier, vol. 129(C), pages 181-197.
    8. Ritesh Jain & Michele Lombardi, 2019. "Virtual implementation by bounded mechanisms: Complete information," IEAS Working Paper : academic research 19-A001, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    9. Siyang Xiong, 2022. "Nash implementation by stochastic mechanisms: a simple full characterization," Papers 2211.05431, arXiv.org.

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    More about this item

    Keywords

    : Implementation; Social choice correspondences; Monotonicity; Rationalizability;
    All these keywords.

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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